Equivalent Expressions and Fraction Notation

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  • 0:02 Equivalent Fractions
  • 1:45 Practice
  • 3:30 Simplifying
  • 5:11 Lesson Summary
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Lesson Transcript
Instructor: Jeff Calareso

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

Did you know that two fractions can look completely different, but actually be the same? In this lesson, we'll learn about equivalent fractions. We'll also learn to simplify fraction notation.

Equivalent Fractions

We're going to learn about equivalent fractions, so let's talk pizza. Your friends Max and Daisy are each offering to share their pizza with you. Max says you can have 2 slices of pizza. Daisy says you can have 4 slices of hers.

Max and Daisy are trying to buy your friendship with pizza. There are worse ways, sure. But who is offering the better deal? Max's pizza only has 4 slices. So he's offering you 2/4 of his pizza. That's a fraction. Daisy's pizza has 8 slices. So, she's offering you 4/8 of her pizza.

2/4 and 4/8. When you put them next to each other, it looks like the same amount either way, right? And, in fact, it is. 2/4 and 4/8 are equivalent fractions. These are fractions with the same value.

We can see it in pizza form, but, well, while we're talking about this I kind of ate most of the pizza. Sorry about that. But can we understand it in math terms?

Let's multiply 2/4 by 2/2. 2 * 2 is 4 and 4 * 2 is 8. So, now we have 4/8. Now, why could we do that? Well, 2/2 is the same as 1. If you have one pizza and you multiply it by 1, sadly, you still only have one pizza.

With fractions, we can multiply them by any version of 1, like 2/2, 3/3, 847/847, and the new fraction will look different, but it will be equivalent to our original fraction. So, Daisy wasn't offering us more pizza; she just cut hers into smaller pieces.


You might see an equivalent fraction problem that looks like this: 7/8 = x/40. We want to solve for x, and there are a few ways we do this.

First, remember that our second fraction must be 7/8 * 1. We just need to figure out what fraction is used. Well, 8 times what is 40? 8 * 5 is 40. So, it must be 5/5. To find x, we just multiply 7 * 5. That's 35. So, 7/8 = 35/40. And that's it!

Also, a 40-slice pizza? That's a big pizza, or little slices. If Daisy said she'd give you 35 slices, but they're all the size of a pepperoni slice, well, I guess that's still a lot of pizza.

Anyway, we could also solve this problem by cross multiplying. We could do 7 * 40 = 8x. 7 * 40 is 280. 280 / 8 is 35. Again, 35 tiny pizza slices.

Equivalent fractions aren't always about making fractions bigger through multiplication; sometimes we need division. Look at this one: 3/9 = x/3.

This time, we want to make the fraction smaller. Let's use a number line to visualize this. Here's what 3/9 looks like. We have a bar divided into 9 segments and 3 are highlighted.

What 3/9 looks like on a number line
number line split into 1/9 increments

Here's an equivalent bar with just 3 segments.

3/9 is equivalent to 1/3
number line for 1/9 and number line for 1/3

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